function [y z t] = Resultant_Solver_DLS(f1coeff,f2coeff,f3coeff)
u = round(randn(4,1) * 100);
M2 = cayley_LS_M(f1coeff, f2coeff, f3coeff,u);

% construct the multiplication matrix via schur compliment of the Macaulay
% matrix
Mtilde = M2(1:27,1:27) - M2(1:27,28:120)/M2(28:120,28:120)*M2(28:120,1:27);

[V,~] = eig(Mtilde); 

% extract the optimal solutions from the eigen decomposition of the
% Multiplication matrix

sol =  V([10 4 2],:)./(ones(3, 1)*V(1,:));

if (find(isnan(sol(:))) > 0)

    x = [];
    y = [];
    z = [];
else

    I = find(not(imag( sol(1,:) )));
    y = sol(1,I);
    z = sol(2,I);
    t = sol(3,I);
end

end

function M = cayley_LS_M(a,b,c,u) %,u1,u2,u3)
% Construct the Macaulay resultant matrix

M = [u(1) 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 a(1) 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 b(1) 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 c(1) 0; u(4) u(1) 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 a(1) a(10) 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 b(1) 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 b(10) 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 c(1) 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 c(10) 0; 0 u(4) u(1) 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 a(10) a(14) 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 a(1) 0 0 b(10) 0 0 0 0 0 0 0 0 0 0 b(1) 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 b(14) 0 0 0 0 0 c(1) 0 0 0 0 0 0 0 0 0 c(10) 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 c(14) 0; u(3) 0 0 u(1) 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 a(11) 0 0 0 0 0 0 0 0 0 0 0 0 0 a(1) 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 b(1) 0 0 0 0 0 0 b(11) 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 c(11) c(1); 0 u(3) 0 u(4) u(1) 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 a(11) a(5) 0 0 0 0 0 0 0 a(1) 0 0 0 0 0 a(10) 0 0 0 0 b(11) 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 b(1) 0 0 0 0 b(10) 0 0 0 0 0 0 b(5) 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 c(11) c(1) 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 c(5) c(10); 0 0 u(3) 0 u(4) u(1) 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 a(5) a(12) 0 0 0 0 0 a(1) 0 a(10) 0 0 0 0 0 a(14) 0 a(11) 0 0 b(5) 0 0 0 0 0 0 0 b(1) 0 0 b(11) 0 0 0 0 0 b(10) 0 0 0 0 b(14) 0 0 0 0 0 0 b(12) 0 0 0 0 0 c(11) 0 0 0 0 0 0 0 0 0 c(5) c(10) 0 0 0 0 0 0 0 0 0 0 c(1) 0 0 0 0 0 0 c(12) c(14); 0 0 0 u(3) 0 0 u(1) 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 a(1) 0 0 0 0 a(15) 0 0 0 0 0 0 0 0 0 0 0 0 0 a(11) 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 b(1) b(11) 0 0 0 0 0 0 b(15) 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 c(1) 0 0 0 0 0 0 0 0 0 0 c(15) c(11); 0 0 0 0 u(3) 0 u(4) u(1) 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 a(10) 0 0 0 a(15) a(6) 0 0 0 0 0 0 0 a(11) 0 a(1) 0 0 0 a(5) 0 0 0 0 b(15) 0 0 0 0 0 0 0 0 b(1) 0 0 0 0 0 0 0 b(11) 0 0 0 b(10) b(5) 0 0 0 0 0 0 b(6) 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 c(15) c(11) 0 0 0 0 0 0 c(10) 0 0 0 0 c(1) 0 0 0 0 0 c(6) c(5); 0 0 0 0 0 u(3) 0 u(4) u(1) 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 a(14) 0 0 0 a(6) 0 0 0 0 0 0 a(11) 0 a(5) 0 a(10) a(1) 0 0 a(12) 0 a(15) 0 0 b(6) 0 0 0 0 0 0 0 b(11) b(10) 0 b(15) b(1) 0 0 0 0 b(5) 0 0 0 b(14) b(12) 0 0 0 0 0 0 0 0 0 0 0 0 c(15) 0 0 0 0 0 0 0 0 0 c(6) c(5) 0 c(1) 0 0 0 0 c(14) 0 0 0 c(11) c(10) 0 0 0 0 0 0 c(12); u(2) 0 0 0 0 0 0 0 0 u(1) 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 a(9) a(1) 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 b(9) b(1) 0 0 0 c(1) 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 c(9) 0; 0 u(2) 0 0 0 0 0 0 0 u(4) u(1) 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 a(1) a(9) a(4) a(10) 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 b(9) 0 0 0 0 b(1) 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 b(4) b(10) 0 0 0 c(10) 0 0 0 0 0 0 0 0 0 0 c(9) 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 c(1) c(4) 0; 0 0 u(2) 0 0 0 0 0 0 0 u(4) u(1) 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 a(1) 0 0 0 0 a(10) a(4) a(8) a(14) 0 0 0 0 0 0 0 0 0 0 0 0 0 0 a(9) 0 0 b(4) 0 0 b(1) 0 b(10) 0 0 0 0 0 b(9) 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 b(8) b(14) 0 0 0 c(14) c(9) 0 0 0 0 0 0 0 0 0 c(4) 0 0 0 0 0 0 0 0 0 0 0 0 0 0 c(1) 0 0 c(10) c(8) 0; 0 0 0 u(2) 0 0 0 0 0 u(3) 0 0 u(1) 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 a(3) a(11) 0 0 a(1) 0 0 0 0 0 0 0 0 0 a(9) 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 b(9) 0 0 b(1) 0 0 0 b(3) b(11) 0 0 0 c(11) 0 0 0 0 0 0 0 c(1) 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 c(3) c(9); 0 0 0 0 u(2) 0 0 0 0 0 u(3) 0 u(4) u(1) 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 a(11) a(3) a(17) a(5) 0 0 a(10) 0 0 0 a(9) 0 0 0 a(1) 0 a(4) 0 0 0 0 b(3) 0 0 0 0 b(11) b(1) 0 0 0 0 0 0 0 0 0 0 b(9) 0 0 0 0 b(4) 0 0 b(10) 0 0 0 b(17) b(5) 0 0 0 c(5) 0 c(1) 0 0 0 0 0 c(10) 0 0 c(3) c(9) 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 c(11) c(17) c(4); 0 0 0 0 0 u(2) 0 0 0 0 0 u(3) 0 u(4) u(1) 0 0 0 0 0 0 0 0 0 0 0 0 0 a(11) 0 0 0 0 a(5) a(17) 0 a(12) 0 0 a(14) 0 a(9) a(1) a(4) 0 0 0 a(10) 0 a(8) 0 a(3) 0 0 b(17) 0 b(1) b(11) 0 b(5) b(10) 0 b(9) 0 0 b(3) 0 0 0 0 0 b(4) 0 0 0 0 b(8) 0 0 b(14) 0 0 0 0 b(12) 0 0 0 c(12) c(3) c(10) 0 0 0 0 0 c(14) 0 0 c(17) c(4) 0 0 0 0 0 c(1) 0 0 0 0 c(9) 0 0 c(11) 0 0 c(5) 0 c(8); 0 0 0 0 0 0 u(2) 0 0 0 0 0 u(3) 0 0 u(1) 0 0 0 0 0 0 0 0 0 0 0 0 0 a(1) a(9) 0 0 0 0 a(18) a(15) 0 0 a(11) 0 0 0 0 0 0 0 0 0 a(3) 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 b(1) b(9) b(3) 0 0 b(11) 0 0 0 b(18) b(15) 0 0 0 c(15) 0 0 0 0 0 c(1) 0 c(11) 0 0 0 0 0 0 0 0 0 0 c(9) 0 0 0 0 0 0 0 0 0 0 c(18) c(3); 0 0 0 0 0 0 0 u(2) 0 0 0 0 0 u(3) 0 u(4) u(1) 0 0 0 0 0 0 0 0 0 0 0 0 a(10) a(4) 0 0 a(15) a(18) 0 a(6) 0 0 a(5) 0 0 0 a(3) a(1) a(9) 0 a(11) 0 a(17) 0 0 0 0 b(18) 0 0 0 0 b(15) b(11) 0 0 b(9) 0 0 0 0 b(1) 0 0 b(3) 0 0 b(10) b(4) b(17) 0 0 b(5) 0 0 0 0 b(6) 0 0 0 c(6) 0 c(11) 0 0 0 c(10) 0 c(5) c(1) 0 c(18) c(3) 0 0 0 0 0 0 c(4) 0 0 0 0 c(9) 0 0 0 0 c(15) 0 c(17); 0 0 0 0 0 0 0 0 u(2) 0 0 0 0 0 u(3) 0 u(4) u(1) 0 0 0 0 0 0 0 0 0 0 a(15) a(14) a(8) 0 0 a(6) 0 0 0 0 0 a(12) 0 a(3) a(11) a(17) a(10) a(4) a(9) a(5) 0 0 0 a(18) 0 0 0 0 b(11) b(15) 0 b(6) b(5) 0 b(3) b(4) 0 b(18) b(9) 0 b(10) 0 0 b(17) 0 0 b(14) b(8) 0 0 0 b(12) 0 0 0 0 0 0 0 0 0 c(18) c(5) 0 0 0 c(14) 0 c(12) c(10) 0 0 c(17) 0 c(9) 0 0 0 c(11) c(8) 0 0 0 c(3) c(4) 0 c(15) 0 0 c(6) 0 0; 0 0 0 0 0 0 0 0 0 u(2) 0 0 0 0 0 0 0 0 u(1) 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 a(13) a(9) 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 a(1) 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 b(1) b(13) b(9) 0 0 c(1) c(9) 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 c(13) 0; 0 0 0 0 0 0 0 0 0 0 u(2) 0 0 0 0 0 0 0 u(4) u(1) 0 0 0 0 0 0 0 0 0 0 0 0 a(1) a(9) a(13) a(19) a(4) 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 a(10) b(13) 0 0 0 0 b(9) 0 b(1) 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 b(10) b(19) b(4) 0 0 c(10) c(4) 0 0 0 0 0 0 0 0 0 0 c(13) 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 c(1) c(9) c(19) 0; 0 0 0 0 0 0 0 0 0 0 0 u(2) 0 0 0 0 0 0 0 u(4) u(1) 0 0 0 0 0 0 a(1) a(9) 0 0 0 a(10) a(4) a(19) 0 a(8) 0 0 0 0 0 0 0 0 0 0 0 0 0 0 a(13) 0 a(14) b(19) b(1) 0 b(9) 0 b(4) 0 b(10) 0 0 0 b(13) 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 b(14) 0 b(8) 0 0 c(14) c(8) c(13) 0 0 0 0 0 0 0 0 0 c(19) 0 0 0 0 0 0 0 0 0 0 0 0 0 c(1) c(9) 0 c(10) c(4) 0 0; 0 0 0 0 0 0 0 0 0 0 0 0 u(2) 0 0 0 0 0 u(3) 0 0 u(1) 0 0 0 0 0 0 0 0 0 0 0 0 0 a(2) a(3) 0 a(1) a(9) 0 0 0 0 0 0 0 0 0 a(13) 0 0 0 a(11) 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 b(13) 0 b(1) b(9) 0 0 b(11) b(2) b(3) 0 0 c(11) c(3) 0 0 0 c(1) 0 0 0 c(9) 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 c(2) c(13); 0 0 0 0 0 0 0 0 0 0 0 0 0 u(2) 0 0 0 0 0 u(3) 0 u(4) u(1) 0 0 0 0 0 0 0 0 0 a(11) a(3) a(2) 0 a(17) 0 a(10) a(4) a(1) 0 0 a(13) 0 0 0 a(9) 0 a(19) 0 0 0 a(5) b(2) 0 0 0 0 b(3) b(9) b(11) 0 0 0 0 0 0 0 0 0 b(13) b(1) 0 0 0 b(19) 0 b(10) b(4) 0 0 b(5) 0 b(17) 0 0 c(5) c(17) 0 c(9) 0 c(10) 0 0 c(1) c(4) 0 0 c(2) c(13) 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 c(11) c(3) 0 c(19); 0 0 0 0 0 0 0 0 0 0 0 0 0 0 u(2) 0 0 0 0 0 u(3) 0 u(4) u(1) 0 0 0 a(11) a(3) 0 0 0 a(5) a(17) 0 0 0 0 a(14) a(8) a(10) a(13) a(9) a(19) 0 0 0 a(4) 0 0 0 a(2) 0 a(12) 0 b(11) b(9) b(3) 0 b(17) b(4) b(5) b(13) 0 0 b(2) 0 0 0 0 0 b(19) b(10) 0 0 0 0 0 b(14) b(8) 0 0 b(12) 0 0 0 0 c(12) 0 c(2) c(4) 0 c(14) 0 0 c(10) c(8) 0 0 0 c(19) 0 0 0 0 0 c(9) 0 0 0 0 c(13) 0 c(11) c(3) 0 c(5) c(17) 0 0; 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 u(2) 0 0 0 0 0 u(3) 0 0 u(1) 0 0 0 0 a(9) a(13) 0 0 0 0 0 a(18) 0 a(11) a(3) 0 0 0 0 0 0 0 0 0 a(2) 0 0 a(1) a(15) 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 b(1) b(9) b(13) b(2) 0 b(11) b(3) 0 0 b(15) 0 b(18) 0 0 c(15) c(18) 0 0 0 c(11) c(1) c(9) 0 c(3) 0 0 0 0 0 0 0 0 0 0 c(13) 0 0 0 0 0 0 0 0 0 0 0 c(2); 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 u(2) 0 0 0 0 0 u(3) 0 u(4) u(1) 0 0 0 a(4) a(19) 0 a(15) a(18) 0 0 0 0 a(5) a(17) a(11) 0 0 a(2) a(9) a(13) 0 a(3) 0 0 0 0 a(10) a(6) 0 0 0 0 0 b(18) b(3) b(15) 0 b(13) 0 0 0 0 b(9) 0 0 b(2) b(11) b(10) b(4) b(19) 0 0 b(5) b(17) 0 0 b(6) 0 0 0 0 c(6) 0 0 c(3) 0 c(5) c(10) c(4) c(11) c(17) c(9) 0 0 c(2) 0 0 0 0 0 0 c(19) 0 0 0 0 c(13) 0 0 0 c(15) c(18) 0 0; 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 u(2) 0 0 0 0 0 u(3) 0 u(4) u(1) a(15) a(18) a(8) 0 0 a(6) 0 0 0 0 0 a(12) 0 a(5) a(2) a(3) 0 a(4) a(19) a(13) a(17) 0 0 0 0 a(14) 0 0 b(15) b(3) b(18) 0 0 b(17) b(6) b(2) b(19) 0 0 b(13) 0 b(4) 0 0 0 b(5) b(14) b(8) 0 0 0 b(12) 0 0 0 0 0 0 0 0 0 0 0 c(17) 0 c(12) c(14) c(8) c(5) 0 c(4) 0 0 0 0 c(13) 0 0 0 c(3) 0 0 0 0 c(2) c(19) c(15) c(18) 0 c(6) 0 0 0; 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 u(3) 0 0 0 0 0 0 0 0 0 0 0 0 0 a(11) a(3) 0 0 0 0 0 a(7) 0 0 a(15) 0 0 0 0 0 0 0 0 0 a(18) 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 b(9) b(1) 0 0 0 b(11) b(3) b(18) 0 0 b(15) 0 0 0 0 b(7) 0 0 0 c(7) 0 0 c(1) 0 0 c(11) 0 c(15) 0 0 0 0 0 0 0 0 0 0 c(3) 0 0 c(9) 0 0 0 0 0 0 0 0 c(18); 0 0 0 0 0 0 u(3) 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 a(11) 0 0 0 0 a(7) 0 0 0 0 0 0 0 0 0 0 0 0 0 a(15) 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 b(1) 0 0 0 0 0 b(11) b(15) 0 0 0 0 0 0 b(7) 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 c(11) 0 0 c(1) 0 0 0 0 0 0 0 c(7) c(15); 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 u(3) 0 0 0 0 a(3) a(2) 0 0 0 0 0 0 0 a(15) a(18) 0 0 0 0 0 0 0 0 0 0 0 0 a(11) a(7) 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 b(13) b(9) 0 0 b(11) b(3) b(2) 0 0 b(15) b(18) 0 0 b(7) 0 0 0 0 c(7) 0 0 0 c(9) c(15) c(11) c(3) 0 c(18) 0 0 0 0 0 0 0 0 0 0 c(2) 0 0 c(13) 0 0 0 0 0 0 0 0 0; 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 a(18) 0 0 0 0 0 0 0 0 0 0 a(7) 0 0 0 a(2) 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 b(20) 0 0 b(2) 0 0 0 b(18) 0 0 0 b(7) 0 0 0 c(7) 0 0 0 0 0 c(20) 0 c(2) 0 0 0 0 c(18) 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0; 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 a(2) 0 0 0 0 0 0 0 a(15) a(18) 0 0 0 0 0 0 0 0 0 0 0 a(7) 0 a(3) 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 b(20) b(13) 0 0 b(3) b(2) 0 0 b(15) b(18) 0 b(7) 0 0 0 0 0 c(7) 0 0 0 0 c(13) c(18) c(3) c(2) 0 0 0 c(15) 0 0 0 0 0 0 0 0 0 0 0 c(20) 0 0 0 0 0 0 0 0 0; 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 a(9) 0 a(13) 0 0 a(20) 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 b(13) b(9) b(20) 0 0 c(9) c(13) c(20) 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0; 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 a(15) a(18) 0 0 0 0 0 0 0 0 a(7) 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 b(9) 0 0 0 0 b(3) b(11) 0 0 0 b(15) b(18) 0 0 0 b(7) 0 0 0 0 0 0 0 0 0 0 0 c(11) 0 0 c(15) 0 c(7) 0 0 0 0 0 0 c(9) 0 0 0 c(18) 0 0 c(3) 0 0 0 0 0 0 0 0 0; 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 a(18) 0 0 0 0 0 0 0 0 a(7) 0 0 0 0 0 0 0 0 0 0 0 0 0 a(15) 0 0 0 0 0 0 0 0 0 0 0 b(13) 0 0 0 0 b(2) b(3) 0 0 b(15) b(18) 0 0 0 b(7) 0 0 0 0 0 0 0 0 0 0 0 0 c(3) c(7) c(15) c(18) 0 0 0 0 0 0 0 0 c(13) 0 0 0 0 0 0 c(2) 0 0 0 0 0 0 0 0 0; 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 a(7) 0 0 0 0 0 0 0 0 0 0 0 0 0 0 a(18) 0 0 0 0 0 0 0 0 0 0 0 b(20) 0 0 0 0 0 b(2) 0 0 b(18) 0 0 0 b(7) 0 0 0 0 0 0 0 0 0 0 0 0 0 c(2) 0 c(18) 0 0 0 0 c(7) 0 0 0 0 c(20) 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0; 0 0 0 0 0 u(4) 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 a(12) 0 0 0 0 0 0 a(10) 0 a(14) 0 0 0 0 0 a(16) 0 a(5) 0 0 b(12) 0 0 0 0 0 0 0 b(10) 0 0 b(5) 0 0 0 0 0 b(14) 0 0 0 0 b(16) 0 0 0 0 0 0 0 0 0 0 0 0 c(5) 0 0 0 0 0 0 0 0 0 c(12) c(14) c(1) 0 0 0 0 0 0 0 c(11) 0 c(10) 0 0 0 0 0 0 0 c(16); 0 0 u(4) 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 a(14) a(16) 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 a(10) 0 0 b(14) 0 0 0 0 0 0 0 0 0 0 b(10) 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 b(16) 0 0 0 0 0 c(10) 0 0 0 0 0 0 0 0 0 c(14) 0 0 0 0 0 0 0 0 0 c(1) 0 0 0 0 0 0 0 0 c(16) 0; 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 a(15) 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 a(7) 0 0 0 0 0 0 0 0 0 0 0 0 0 0 b(1) 0 0 0 0 b(11) 0 0 0 0 0 b(15) b(7) 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 c(1) 0 0 0 c(15) 0 0 c(11) 0 0 0 0 0 0 0 0 c(7); 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 a(14) 0 0 0 0 a(16) 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 a(8) 0 0 0 0 0 b(14) 0 b(16) 0 0 0 0 0 b(8) 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 c(8) 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 c(9) 0 0 c(10) c(4) 0 0 0 0 c(14) 0 0 c(16) 0 0; 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 a(14) a(8) 0 0 0 a(16) 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 b(14) 0 b(8) 0 0 0 b(16) 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 c(13) 0 0 c(4) c(19) 0 0 0 c(14) c(8) 0 c(16) 0 0 0; 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 a(7) 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 b(11) 0 0 0 0 b(15) 0 0 0 0 0 b(7) 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 c(11) 0 0 0 c(7) 0 0 c(15) 0 0 0 0 0 0 0 0 0; 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end